KR20120072290A - Method for analyzing incremental non-guassian - Google Patents

Abstract

PURPOSE: A method for analyzing incremental non-Gaussian time is provided to minimize memory usage and data processing time by utilizing incremental ICA(Independent Component Analysis) scheme by analysis of EEG(Electroencephalography) signal data. CONSTITUTION: First input vector data is composed of matrices. The first input vector data is represented and disassembled into a non-Gaussian weight vector. The non-Gaussian weight vector is updated by the second input vector data. The non-Gaussian weight vector is repeated until maximum non-Gaussian characteristics are indicated.

Description

Gradual Non-Gaussian Analysis Method {METHOD FOR ANALYZING INCREMENTAL NON-GUASSIAN}

The present invention relates to a gradual non-time analysis method, and more particularly, to process the data in each input vector to find potential variables in the analysis of physiological signal data, such as multivariate electroencephalography (EGE) signals A method for data analysis using progressive independent component analysis that minimizes memory usage and data processing time by utilizing progressive independent component analysis, in which data is stored as several variables and the previous values of the variables are updated by later input vectors. will be.

In recent decades, interest in multivariate data mining has increased dramatically. As modern information technology advances, large volumes of multivariate data are becoming important in different areas, from finance, engineering, and medicine to science. It is essential to design data that collects data on several variables so that they are closely related to each other in various ways.

As the research on multivariate data mining diversifies, research on mining large data sets including one or more variables is being activated. This is to search for useful information and to provide useful decisions with huge amounts of multivariate data.

Typically, in many practical applications, the data tables being analyzed consist of several measurements collected on a series of units (eg subjects, samples). For example, in microarray chips, a wide range of genes are collected in a single experiment. Gene expressions are identified through experiments. Another example is the EEG signal, in which a large number of signals are obtained from the brain cortex. The signals are collected at high frequencies and the data set is of a very high dimension.

DNA microarrays are devices that can be used to simultaneously measure the presence of mRNAs for large numbers of genes in a single experiment. High-level microarray gene expression has been an obstacle for biologists to have comprehensive insights into microarray data.

The unique presence of microarray data, which includes many features but a relatively small number of observations, contrasts with the normal behavior of most real-world data. Moreover, the gene expressions of the two individuals are rarely the same.

Genetically modified genes are becoming more challenging to analyze microarray data. Moreover, during the microarray experiments, data tends to be noisy from tissue collection, amplification of mRNA for hybridization on the chip.

Time series microarray experiments are commonly used to characterize the active biological processes of genes between time series. The ability to analyze large numbers of genes in one experiment encourages biologists to collect more samples from microarray data.

Therefore, it is expected that the data of many patients will be useful in the future. Moreover, with the development of modern technology, more genes may be discovered by biologists. Thus, both the number of samples and the number of genes are expected to grow.

Thus, the size of the microarray data will continue to increase. In this case, a suitable method would be proposed to solve the problem of huge data dimensions by retaining important information and by removing contaminated noise.

The EEG signal is an example of a data stream in which signals of continuous flow arrive successfully at a high rate. Data is collected from sensors attached to the brain cortex. High speed electrical data collected from multiple sensors tends to form a high dimension.

Traditional systems are slow to process the time associated with the EEG signal and often cannot provide immediate processing, which is important for decision making. With the successful arrival of electrical signals, rapid processing of high speed data is important. Moreover, given the current computational power, it is impossible to retain all previous data in the allocated memory.

EEG signals are considered to be intrinsically interrelated between the sensors and it is possible to discover patterns and correlations between them. While EEG signals are collected, EEG signals include inevitable artifacts obtained from leads and devices used to collect and visualize the signal.

Such noise is undesirable because it affects the results. Therefore, while detecting the correlation of data online, it is important to remove noise from such data.

As its name suggests, multivariate analysis involves a set of techniques suitable for analysis of data sets with more than one variable. These techniques have been developed in the field of multivariate analysis because it is important to find results that take into account relationships between multiple variables as well as within variables.

Multivariate analysis is widely used to extract features and to reduce dimension and EEG signals of microarray data sets.

Principal component analysis (PCA) is the most common multivariate analysis of dimension reduction. Summarizing time series microarray data and reducing the dimensions of the EEG data set are studied.

Independent component analysis is another method in multivariate statistical analysis to separate data into basic information components. ICA is an indispensable useful way of identifying the driving forces underlying a series of observed phenomena. These phenomena include firing a series of neurons and microarray data sets from the brain. ICA is applied to many applications such as separation, visualization, localization and extraction of features of EEG signals from MEG data.

While PCA finds a series of signals that are much weaker than independence, ICA discovers a series of independent source signals. In particular, the PCA finds a series of signals that are not related to each other.

In some cases, if the data is Gaussian, the estimation of the model requires an orthogonal transformation. However, PCAs require orthogonality for real world data, not Gaussian distributions.

In probability theory, the central limit theory (CLT) refers to conditions under which the sum of sufficiently large independent random variables is approximately normally distributed. That is, mixtures of some sources tend to be more Gaussian than the distribution of the original sources. If their components are Gaussian, the PCA provides a series of independent components. Conversely, ICA is considered a non-Gaussian factor analysis in which ICA decomposes statistical independent components. Many studies show that ICA outperforms PCA in microarray and EEG signals analysis.

More applications are emerging with large scale microarray and EEG signal data sets. It is important to analyze the data as soon as it arrives. Unfortunately, conventional methods of processing microarray data sets and EEG signals always process this data in a static state. In addition, especially for time series data, the batch processing depends on the holding time t, which increases to infinity.

Both conventional PCA and ICA include computation of singular value decomposition (SVD), which consumes huge memory. Since the space requirement also depends on the holding time t, the consumption of space is proportional to the holding time t. Therefore, batch mode processing always entails a large memory requirement and is time consuming, especially when the size of the data increases. In other words, it is impossible for ICA to process multivariate data when the retention time increases infinitely.

The problem to be solved by the present invention is to overcome the above problems, to provide a gradual non-time analysis method that can minimize the memory usage and data processing time by using a progressive independent component analysis technique in multivariate EEG signal data analysis It is.

Another problem to be solved by the present invention is to overcome the above problems, by successfully incorporating a non-normal and adaptive gradual model to successfully extract the EEG signal features, thereby having a data feature significantly greater than the number of observed data It is to provide a gradual rain time analysis method that can also be analyzed for microarray gene expression data.

The present invention relates to a progressive non-corruption time analysis method, comprising: (a) constructing input first input vector data into a matrix; (b) normalizing the first input vector data consisting of a matrix and decomposing it into a non-Gaussian weight vector; And (c) updating the non-Gaussian weight vector with second input vector data that is then input; It includes.

Preferably, the first and second input vector data is microarray gene expression data or EEG (Electroencephalography) signal data.

Also preferably, the step (b) includes (b-1) projecting the non-Gaussian weight vector on the first input vector by linear transformation to derive a hidden variable. .

Also preferably, step (c) comprises: (c-1) calculating a hidden variable from the second input vector using the non-Gaussian weight vector of step (b); And (c-2) estimating energy by the following equation using the hidden variable calculated in step (c-1); Characterized in that it comprises a.

(In the above equation, d _i is energy, λ is forgetting factor, y _i is a hidden variable calculated in step (c1).)

Also preferably, the forgetting factor λ is selected from 0.96 to 0.98.

Also preferably, the energy d _i is characterized in that determined in 95% to 98%.

And preferably, after step (c), repeating step (c) until the updated non-Gaussian weight vector exhibits a maximum non-Gaussian feature. It is done.

According to the present invention, in the analysis of multivariate EEG signal data, it is possible to minimize memory usage and data processing time by using a progressive independent component analysis technique.

According to the present invention, it is possible to successfully extract EEG signal features by incorporating a nonnormal and adaptive gradual model, thus analyzing effects on microarray gene expression data having data features significantly greater than the number of observed data. There is also.

1 is a diagram illustrating a non-Gaussian analysis algorithm fragment.
2 is a diagram illustrating hierarchical clustering of the method (a), progressive PCA (b), ICA (c) and PCA (d) outputs according to the present invention.
3 shows hierarchical clustering of normalized raw data (a), data (b) reproduced by the method according to the invention, progressive PCA (c), ICA (d) and PCA (e).
4A shows the execution time for the number of genes on a microarray data set.
4B is a diagram illustrating an execution time for the number of sources on an EEG signal data set.
5A is a diagram showing execution time for the number of experiments in microarray data.
5B is a diagram illustrating an execution time with respect to a stream size in EEG signal data.

Prior to describing the specific details for carrying out the invention, the terminology or words used in this specification and claims may properly define the concept of a term in order for the inventor to best describe his or her invention. It should be interpreted as meaning and concept corresponding to the technical idea of the present invention on the basis of the principle.

In addition, when it is determined that the detailed description of the known function and its configuration related to the present invention may unnecessarily obscure the subject matter of the present invention, it should be noted that the detailed description is omitted.

The present invention relates to an analytical method incorporating a gradual approach to independent component analysis (ICA) techniques in multivariate EEG signal data analysis.

According to the method according to the invention, orthogonal weights are calculated by updating each weight vector in a predetermined energy range. When obtaining an orthogonal weight, it converges to be a non-Gaussian weight.

Then, when new data is input, instead of recalculating all the data sets, working gradually in a manner of updating non-Gaussian weights using old variables, resulting in lower computational costs.

The method according to the invention adapts the concept of statistically converging the independent components of multivariate data in a gradual approach. The conventional batch calculation method requires a complete data matrix recalculation when new data is input, which requires unnecessary memory usage and processing time, while the method according to the present invention uses the past variables without including the complete data matrix. The new arrival data can be efficiently updated.

Hereinafter, independent component analysis will be described in detail before describing the gradual non-corruption analysis method according to the present invention.

Independent component analysis (ICA) is a method for finding basic components from multidimensional data. A series of components that are most independent of each other is determined by higher level statistics. ICA is widely used for EEG signal analysis.

Hereinafter, an EEG signal will be described as an example, but independent component analysis or the present invention is not limited thereto.

In EEG signal analysis, simultaneous neural sources that collaborate on a particular response are collected via sensors. Many signals are obtained by sensors attached to areas of the brain cortex. These signals are a mixture of the original neural signals from the brain.

이 진폭이고, t가 시간 지표일 때, 센서들로부터의 신호를

로 표시하자. 이렇게 기록된 신호들 각각은

로 표시되는 뇌신경에 의해 발산된 신경 신호들의 가중 합계이다. 이는 다음의 [수학식 1]과 같은 선형 방정식으로서 표현될 수 있다.

Is amplitude and t is a time indicator,

Let's mark Each of these recorded signals

It is the weighted sum of neural signals emitted by the cranial nerve. This can be expressed as a linear equation such as [Equation 1] below.

[Equation 1]

은 뇌신경들로부터 센서들의 거리들 또는 조건들에 의존하는 파라미터들이다. 간단히, [수학식 1]과 같은 선형 방정식은 다음의 [수학식 2]와 같이 표현될 수 있다.In Equation 1

Are parameters that depend on the distances or conditions of the sensors from the cranial nerves. For simplicity, a linear equation such as Equation 1 may be expressed as Equation 2 below.

[Equation 2]

x = As

Generally, bold lowercase letters represent vectors and bold uppercase letters represent matrices.

The task of the ICA is to find such A where the source signals or components s are statistically independent. After estimating the matrix A , its inverse W can be calculated to obtain independent components as shown in Equations 3 and 4.

&Quot; (3) "

&Quot; (4) "

The model can also be expressed as Equation 5 below.

[Equation 5]

It is the assumptions of the ICA model that the components s are statistically independent and that the independent components must have a non-Gaussian distribution. Consider y, a linear combination of s _i , and find one of the independent components (y) as shown in [Equation 6].

&Quot; (6) "

By maximizing the non-Gaussian of W ^T x, the independent component (y) can be obtained.

Fast ICA derives the maximum non-Gaussian of W ^T x based on the fixed point iteration technique. One measurement of non-Gaussian is provided by negentropy. This is based on the information-theoretic quantify of differential entropy.

In order for the projection to maximize the non-Gaussian by using an approximation of negentropy, Fast ICA applies a learning rule to find the direction, or unit vector ( W ).

First, the initial weight vector w is chosen randomly. Then, using the higher dimensional moments such as Equation 7 and Equation 8, the negentrophy is approximated.

[Equation 7]

[Equation 8]

은 [수학식 8]의 도함수이며, 알고리즘은 수렴할 때까지 반복된다.
At this time,

Is a derivative of Equation 8, and the algorithm is repeated until convergence.

Hereinafter, a gradual non-corruption time analysis method according to the present invention will be described in detail.

The method according to the invention decomposes statistically independent non-Gaussian weight vectors. The biological processing underlying the microarray gene expression data is more super-Gaussian than the mixing of original sources.

Only a few genes are altered at each pathological metastasis, since many genes are unaffected, which forms a super-Gaussian distribution. Thus, non-Gaussian analysis is suitable for analyzing microarray gene expression data.

The method according to the invention performs autonomous and hierarchical clustering of AD microarray data sets.

The microarray data (X (m, n)) is composed of a two-dimensional mn matrix. Wherein each row m represents gene profile data and each column n represents gene data.

Microarray data is normalized and normalized to zero mean and unit variance. That is, the microarray data is subtracted by the average value and the microarray data subtracted by the standard deviation is divided.

Prior to the clustering process, the first input vector, gene profile data is decomposed into non-Gaussian weight vectors.

Then, the non-Gaussian weight vectors are updated by reflecting the weight of the second input vector (next input gene profile data).

The update process is repeated by reflecting the last input nth input vector, that is, the weight of the last input gene profile data.

By completing the update processing of the non-Gaussian weight vectors for the microarray data, the final non-Gaussian weight vectors are obtained.

In the present invention, the forgetting factor was determined to be 0.96 and the energy was determined to be 95% to 98%. According to the preprocessing, the final dimension of the microarray data matrix was reduced to four. The data matrix used for clustering is 134. In Table 1, you can find the meaning of each variable.

sign Explanation

Input Vector (Bold Lowercase)

N stream input at time (t)

Weight Matrix (bold capital letters)

i-th engagement weight vector

Number of streams

Number of hidden variables

Vector of Hidden Variables for x _t

Energy estimate of the i hidden parameter

Reproduction error rate

The total energy of the hidden variables up to time t and up to the hidden variable i

Total energy of the hidden variables

Energy of input data (x)

Exponential forgetting factor  f Lower limit predetermined energy  F Upper limit predetermined energy

은 연속적으로 무한히 성장할 수 있는 시간(t)에서 n 차원들 측정 열-벡터이다. 최초 타임스탬프 동안, 기본 벡터는 가중치 벡터(w_i)에 의해 채택된다.In the data stream,

Is the n-dimensional measurement heat-vector at time t that can grow continuously infinitely. During the initial timestamp, the base vector is adopted by the weight vector w _i .

Each weight vector w _i is projected onto the input vector x _{t in} a linear transformation of the data stream to obtain hidden variables or components y _t over time.

The key to the gradual approach according to the invention is to gradually update each of the participation weight vectors w _i at each short time in the newly projected space.

In contrast to progressive PCA, the weight vector of the method according to the invention is non-Gaussian. When obtaining an orthogonal weight vector w _i , each weight vector w _i is updated until a maximum non-Gaussian is obtained.

)를 얻는다.The number of hidden variables k is first initialized to an arbitrary number. Then, at time t with n dimensions, the input vector (

Get)

)에 기반하는 i 번째 성분(y_t,i)을 계산한다.From the input vector, the previous weight (

Calculate the i th component (y _{t, i} ) based on

The calculation of the i th component is represented by the following [Equation 9]. That is, it is calculated by the sum of the weight vectors projected on the input vector at time t.

[Equation 9]

Afterwards, the hidden variable calculated from the previous step is used to estimate the energy d _i and the reproduction error rate e _i . The initial value of energy is a small positive value.

When the hidden variable y _{t, i} is obtained, Equations 10 and 11 are executed.

&Quot; (10) "

&Quot; (11) "

In Equation 10, an exponential forgetting factor λ is introduced to allow new data to be adapted to previous behavior in the data stream. The value of the exponential forgetting factor is between 0 and 1.

When setting λ = 0, no previous data is considered in the following processing. In contrast, if λ = 1, the data stream is at rest. However, this usually does not happen because most data streams flow gradually.

The introduction of [lambda] is useful for reducing huge memory usage because there is no need for buffer space for the entire data stream. The preferred range of exponential forgetting factors is values between 0.96 and 0.98. In order for the data to adapt to past values, the exponential forgetting factor is set to a high value. If the value does not change very much, the result is similar.

및

이다.For the magnitude of the estimates, consider the historical data obtained by the participation weight vector w _i . For this reason, the update is inversely proportional to the current energy E _{t, i} of the i th hidden variable. In other words,

And

to be.

The participation weight vector is updated by Equation 12.

[Equation 12]

After obtaining the participatory weighting estimate, continue to maximize the non-Gaussian equation (7) until convergence. In order to converge to the actual value, the participation weight is updated k times according to the number of elements.

)를 얻는다.Finally, the updated engagement weight (

Get)

With the input vector x, the actual concealment variables y _t are computed at time t by projecting the weighting matrix w.

Next, the energy E _hv is calculated according to the values of the hidden variables. To confirm that there are enough components to represent the data, an energy threshold is applied to determine how many hidden variables are needed.

The energy E _hv held by the concealment variables is compared with the upper limit energy F _E E and the lower limit energy f _E E of the original input data.

), 은닉 변수들(k)의 개수를 증가시킨다. 역으로, 만약 유지된 에너지가 너무 높은 경우(

), 우리는 은닉 변수들(k)의 개수를 감소시킨다. 이에 의해, 은닉 변수들의 에너지가 낮은 에너지 값 및 높은 에너지 값 중 특정 구간 내에 항상 있음이 보장된다.If the hidden variables hold too little energy (

), Increasing the number of hidden variables k. Conversely, if the energy held is too high (

We reduce the number of hidden variables k. By this, it is ensured that the energy of the concealment variables is always within a certain interval of the low energy value and the high energy value.

Each time new data arrives, the update process of the weight vector is repeated and the number of hidden variables is adjusted to retain the energy of the components between the predetermined lower and upper limits. 1 is a diagram illustrating a non-Gaussian analysis algorithm fragment.

Hereinafter, an experiment for verifying the efficiency of the gradual rain time analysis method according to the present invention will be described in detail.

First, in order to verify the effectiveness of the method according to the invention in a microarray data set, experiments were performed using GEO data sets deposited by Blalock et al.

Experiment with GEO data set used in the are as a study to analyze the Alzheimer's disease (Alzheimer Disease, AD) to analyze hippocampal gene expression and changes the severity (severity) of the 31 dedicated microarray samples are University of Kentucky materials Alzheimer's Acquired from the Brain Bank of the Center for Disease Research and Human GeneChips (HG-U133A) and Microarray Suite 5 were used for data collection.

Samples containing significant noise were removed, leaving eight controls and leaving five severe AD samples. Unregulated genes in microarray data often contain little information, so these unregulated genes are removed from the experiment. As a result, 13 samples and 3617 genes for each sample were used as the test subjects.

In addition, the method according to the invention was applied to the EEG signal of Alvin mice provided by Dr. Eamonn Keogh. The EEG signal was tested at 128 Hz, with 21386 samples and 512 features. The number of features corresponds to 4 seconds of EEG registration at 128 Hz, and the data set contains three classes, viz. It has wake, synchronized sleep, and REM sleep.

The original data included missing labels for the last 15 records, for which experiments with missing labels were removed.

(A) of FIG. 2 shows the clustering result for the projection of the microarray on non-Gaussian weight vectors. Control samples and severe AD samples can be clearly distinguished by using a few features.

For comparison with the method according to the invention, experiments with gradual PCA were also performed. The main difference between the method according to the invention and the progressive PCA is that the resolved vector components are not independent. In other words, progressive PCA is similar to PCA except that it operates in a progressive manner.

Experiments with incremental PCA were carried out in the same manner and with the same parameter settings as the experiments for the method according to the invention.

Figure 2 (b) shows the clustering results in the experiment applying a gradual PCA, it can be seen that one AD sample, AD2 can not be accurately clustered.

The experimental results for the method according to the invention can also be compared with the ICA experimental results by Kong et al. 2 (c) shows the clustering result by ICA.

In FIG. 2C, the complete data matrix is performed by the fast ICA algorithm, where the Fast ICA is repeated 50 times to mitigate the instability of the somewhat different results generated from each looping. Eleven ICA potential variables are identified to fully obtain important basic biological information from the original data matrix. Both control samples and severe AD samples can be identified by accurate clusters.

However, comparing ICA with the method according to the present invention, it can be seen that the method according to the present invention can achieve significantly efficient results even with fewer components.

On the other hand, the experimental results for the method according to the present invention can be compared with the PCA, and for such a comparison can be prepared for the PCA results by Kong et al.

In the sense that the variables in the projection space are linear combinations of gene expressions, PCA is a linear projection, and PCA experiments are performed by decomposing the gene expression matrix into principal components with 95.5% of the variables. Principal components with low variables, including noise, are removed from the clustering process.

2 (d) shows the clustering result according to the PCA. The control samples were successfully clustered except for the AD samples, but it can be seen that the AD2 samples were inappropriately clustered.

The inventors then examined the effects of the respective methods described above in identifying AD samples from control samples after reproduction.

Reproduced data were obtained by projecting raw data into potential variables found in the respective methods described above. A comparison was performed on the normalized raw data and the hierarchical clustering results performed on the data reproduced by the respective methods described above.

3 (a) shows a clustering result of normalized raw data. In FIG. 3A, it can be seen that although some AD samples are clustered together, the higher layer of the cluster does not successfully identify two different clusters.

In the method according to the invention, a four-dimensional non-Gaussian weight vector obtained by progressively updating the weight vectors in each data observation using 0.96 as the exponential forgetting factor and using 95% to 98% in the energy range. By projecting the data into the furnace, the data are reproduced.

3 (b) shows the clustering result applied to the data reproduced by the method according to the present invention. In FIG. 3 (b), it is clear that the control sample and the AD sample are divided into different groups, and it can be seen that the method according to the present invention can maximize the ability of identifying clustering results. That is, according to the method according to the present invention, even a small number of components can perform a significantly more accurate and efficient clustering than other methods.

3C is a clustering result of the data reproduced by the gradual PCA.

The reproduced data in FIG. 3C is obtained by projecting the raw data onto orthogonal weight vectors obtained from the progressive PCA. For a legitimate comparison, the parameters were set identical to the method according to the invention.

In Figure 3 (c), it can be seen that the gradual PCA does not separate one AD sample, AD2 from the control samples.

For PCA and ICA, 10 principal components and 11 independent components obtained 95.5% of the variables identified as being involved in biological processing are selected to reproduce the data separately. At this time, one AD sample, AD2, is not properly clustered into AD groups by PCA and ICA.

We performed EEG signal separation and demonstrated the superiority of the method according to the invention by comparing the results of the progressive PCA, ICA and PCA results with the method according to the invention. The method according to the invention updates the weight vectors each time a new input arrives to derive hidden variables with non-Gaussian weights. However, ICA and PCA process data in batches.

For simplicity, we performed the experiment using ICA and PCA at the end time, taking into account the overall data flow.

Energy cannot be determined in advance for the ICA. Therefore, the number of components was derived from the PCA to hold 95% of the energy. Progressive PCA derives orthogonal features in a progressive manner by gradually updating orthogonal weights at each time point.

As a classifier, K-Nearest Neighbor (KNN) with K = 1, 2, 3 and Linear Discriminate Analysis (LDA) are adopted. 70% of the data was adopted to train the classifier. The remaining 30% of the data is used for testing. For exponential forgetting factor ([lambda]) and Alvin EEG signals, the energy range is adjusted as shown in [Table 2].

On average, the method according to the invention outperforms other methods. The average classification rate is λ = 0.96, the highest when the energy distribution is between 95% and 98%. Moreover, the method according to the invention achieves the best results under the same conditions and at KNN.

In the case of an LDA classifier, the ICA has the highest classification ratio, which is achieved by the method according to the invention in the case of a parameter λ = 0.98 and an energy range of 95% to 98%. ICA breaks down data into independent, non-Gaussian components.

However, ICA has the disadvantage of including computation of covariance matrices that require high memory. Moreover, the conventional ICA needs to recalculate the entire matrix each time new training data is input.

The method according to the invention stores past values as variables. When new training data is input, the method according to the present invention only requires calculation on variables without having to recalculate the entire matrix, thus saving unnecessary data processing time and memory. In addition, the effect of the method according to the invention can be maximized by appropriate adjustment of the energy range and lambda values.

Moreover, by investigating the number of hidden variables found by the methods described above, the inventors find that the method and the progressive PCA according to the present invention only require fewer data features than PCA and ICA which do not consider a gradual approach. Could. In other words, the method according to the invention is able to achieve more accurate and efficient results even with relatively few features extracted. A small number of data features mean that the amount of computation by the classifiers is relatively small, thus allowing faster classification.

Hereinafter, the effect by the method according to the present invention and the effect by ICA are compared from a qualitative point of view. ICA was chosen for comparison because both methods decompose non-Gaussian components.

Qualitative comparison experiments were performed on Alzheimer's disease microarray data set and EEG signal data set, as these data sets exhibit different behaviors in multivariate data. The composite data is augmented on these data sets to allow more features and more observations to be generated.

4A shows the execution time for the number of genes on a microarray data set. In FIG. 4A, the method according to the invention is shown with asterisk symbols and ICA is shown with plus signs.

In the microarray experiment, the number of observations and other parameter settings were fixed. However, in order for the execution time of different numbers of genes to be recorded in both the method according to the invention and the ICA, the number of genes is increased in each loop. The exponential forgetfulness factor was set to 0.96, with an energy range of 95% to 98% with initial three hidden variables.

In FIG. 4A, as the number of genes increased, run times in both methods increased proportionally. However, it is clear that when the number of genes increases, ICA requires significantly more computation time than the method according to the invention.

4B shows the run time for the number of sources on the EEG signal data set. At this time, the method of performing the experiment was kept the same as the case of the microarray data set as shown in Figure 4a.

In FIG. 4B, as the number of sources is increased, execution time according to ICA increases exponentially. Nevertheless, it can be seen that the execution time by the method according to the invention does not increase dramatically.

The method according to the invention includes only floating operations but ICA involves covariance matrix calculation, so that ICA requires longer computation time when the size of the matrix is increased. Therefore, it is clear that the method according to the invention is more efficient when the number of genes or sources is increased.

5A is a diagram illustrating an execution time for the number of experiments in a microarray data set. At this time, except that the number of genes was fixed, the parameters were set the same as in the above-described experiment. In addition, the number of experiments was changed at each iteration to observe run times of different experiment sizes.

In FIG. 5A, it can be seen that as the number of experiments increases, the execution time does not increase proportionally. This is because when the new experiment involves gene expression, the method according to the invention updates the weight vectors with the new input vector by using the old values stored as variables.

However, as the number of experiments increases, the experimental results for ICA show an extreme upward trend. Moreover, the execution time of the ICA is also significantly greater than the execution time in the method according to the invention.

5B is a diagram illustrating execution time versus stream size for an ICA and a method according to the present invention in an EEG signal data set. At this time, the experimental conditions were set as in the microarray data set.

In FIG. 5B, it is evident that ICA requires an extremely long processing time when the stream size is extremely increased. In contrast, the method according to the invention shows only a slight increase in processing time as the stream size increases.

As described above, according to comprehensive performance verification results in microarrays and EEG signal data sets, etc., the method according to the invention is clearly superior both in the number of data features (genes or sources, etc.) and in the number of observations. It can be seen that it is suitable for both microarray and data stream analysis.

In addition, the method according to the invention can be extended to multi-method data analysis. Multi-modal data analysis is to obtain more diverse behavioral information by finding correlations between different dimensions. At this time, if the method according to the present invention is used, a multi-linear structure can be obtained by gradually using relatively high-dimensional statistics. If the data consists of two or more modes, the basic structures can be detected more efficiently by using a gradual approach in accordance with the present invention.

As described above and described with reference to a preferred embodiment for illustrating the technical idea of the present invention, the present invention is not limited to the configuration and operation as shown and described as described above, it is a deviation from the scope of the technical idea It will be apparent to those skilled in the art that many changes and modifications can be made to the invention without departing from the scope of the invention. Accordingly, all such suitable changes, modifications, and equivalents should be considered to be within the scope of the present invention.

Claims (7)

In the progressive non-corruption time analysis method,
(a) constructing input first input vector data into a matrix;
(b) normalizing the first input vector data consisting of a matrix and decomposing it into a non-Gaussian weight vector; And
(c) updating the non-Gaussian weight vector with second input vector data that is then input; Progressive non-time analysis method comprising a.
The method of claim 1,
And the first and second input vector data are microarray gene expression data or electroencephalography (EEG) signal data.
The method of claim 1,
The step (b)
(b-1) projecting the non-Gaussian weight vector on the first input vector by linear transformation to derive a hidden variable; Progressive non-time analysis method characterized in that it comprises a.
The method of claim 1,
In step (c),
(c-1) calculating a hidden variable from the second input vector using the non-Gaussian weight vector of step (b); And
(c-2) estimating energy by the following equation using the hidden variable calculated in step (c1); Progressive non-time analysis method characterized in that it comprises a.

(In the above equation, d _i is energy, λ is a forgetting factor, y _i is a hidden variable calculated in step (c1).)
The method of claim 4, wherein
And the forgetting factor λ is selected from 0.96 to 0.98.
The method of claim 4, wherein
The energy d _i is determined between 95% and 98%.
The method of claim 1,
After step (c),
(d) repeating step (c) until the updated non-Gaussian weight vector exhibits the largest non-Gaussian feature; Progressive non-time analysis method characterized in that it further comprises.

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